A first-principles plane-wave pseudo potential method based on the density functional theory is used to investigate the phase structures, energies, electronic structures and elastic properties of Ti3AC2 (A=Si, Sn, Al, Ge) phases. In this paper, Ti3AC2 (A=Si, Sn, Al, Ge) crystal structures are first optimized, then the band structures, total and part density of states，charge density distributions and elastic properties of these compounds are analyzed, and the cohesive energies and formation energy of these phases are also calculated. The results show that the Ti3GeC2 is more stable than other compounds, the formation energy of Ti3AlC2 is the lowest in these compounds, which indicates that Ti3AlC2 is easier to generate; Ti3AC2 (A =Si, Sn, Al, Ge) each have a higher density of states at Fermi level, which shows the strong metallicity, meanwhile, the electrical conductivity of each phase is anisotropic. The DOS at the Fermi energy is mainly from the Ti-d electrons, which should be involved in the conduction properties although d electrons are considered to be inefficient conductors. The lowest valence bands are formed by the C-s states with a small mixture of Ti-p+d, and A-s+p states. The electrical properties are mainly decided by the p-d hybridizations between 3d electrons in Ti and the p electrons in A (A =Si, Sn, Al, Ge) and 2p electrons in C, and the strong hybridization of p-d states make the materials have stable structures. It should be noted that the calculated bond length of Ti-Ge is shorter than those of Ti-A (A=Si, Sn, Al) bonds. This implies that the Ti-Ge bond is stronger than Ti-A (A=Si, Sn, Al) bonds. Furthermore, the Fermi level of Ti3GeC2 is relatively low, which also indicates the relatively high stability of Ti3GeC2. The charge density provides a measure of the strength of the ionic bond, so that Ti3GeC2 and Ti3SiC2 have stronger ionic bonds than Ti3SnC2 and Ti3AlC2. The strong M-A bonds in Ti3GeC2 lead to a decreasing and c lattice parameter value increasing. The spherical shape of X represents more like an ionic bond. The z-directional localized shapes of A each is more like a covalent bond. The covalent bonds of A elements each are localized along the z direction so that they affect mostly the c lattice parameter; the calculated elastic properties of Ti3AC2 (A = Si, Sn, Al, Ge) phases show that the atomic binding force of Ti3AlC2 is weaker than those of other three phases, while the atomic binding force of Ti3GeC2 is relatively strong, which makes the strength of Ti3GeC2 quite high.